Optim test

optim_test.jl

# very small subset of data, for testing
       
N = 5 # people
T = 3 # times

data = Float32.([
#    x     y      z
    1.75   0.0    0.75  # person 1 time 1
    2.75   1.75   0.75  # person 1 time 2
    1.25   2.75  -0.75  # person 1 time 3
    1.75   0.0    0.75  # person 2 time 1
    2.0    1.75   0.75  # person 2 time 2
    1.75   2.0   -0.75  # person 2 time 3
    2.25   0.0    0.75  # person 3 time 1
    1.25   2.25  -0.75  # person 3 time 2
    1.5    1.25   0.75  # person 3 time 3
    2.0    0.0   -0.75  # person 4 time 1
    1.75   2.0   -0.75  # person 4 time 2
    1.5    1.75   0.75  # person 4 time 3
    1.25   0.0    0.75  # person 5 time 1
    2.25   1.25  -0.75  # person 5 time 2
    1.0    2.25   0.75  # person 5 time 3
]);


# each person for all the times
person1 = data[1:3,:];
person2 = data[4:6,:];
person3 = data[7:9,:];
person4 = data[10:12,:];
person5 = data[13:15,:];
persons = [person1,person2,person3,person4,person5];

# each time for all the people
time1 = data[[1,4,7,10,13],:];
time2 = data[[1+1,4+1,7+1,10+1,13+1],:];
time3 = data[[1+2,4+2,7+2,10+2,13+2],:];
times = [time1,time2,time3];

# xs ys zs for all people all times
xs = data[:,1];
ys = data[:,2];
zs = data[:,3];

# optimization 

using Optim, LinearAlgebra, StatsBase
using Optim:minimizer

begin
    function f(β, α, xi)
        dot(α, xi) * sum(β)/T
    end;

    function get_β(α, x)
        to_min = β -> begin
            sum(f.(Ref(β), Ref(α), x))
        end
        β_0 = zeros(Float32,N)
        res = optimize(to_min, β_0)
        return minimizer(res)
    end;

    function get_α(x)
        to_min = α -> begin
            β = get_β(α, x)
            # negative cause we want to max
            -mean(f.(Ref(β), Ref(α), x))
        end
        α_0 = zeros(Float32,T)
        res = optimize(to_min, α_0)
        return minimizer(res)
    end
end

optimal_βs = get_β(get_α(persons), persons)

ERROR: DimensionMismatch: x and y are of different lengths!
Stacktrace:
  [1] dot
    @ C:\Users\MrJSa\AppData\Local\Programs\Julia-1.10\share\julia\stdlib\v1.10\LinearAlgebra\src\generic.jl:871 [inlined]
  [2] f(β::Vector{Float32}, α::Vector{Float32}, xi::Float32)
    @ Main .\REPL[70]:3
  [3] _broadcast_getindex_evalf
    @ .\broadcast.jl:683 [inlined]
  [4] _broadcast_getindex
    @ .\broadcast.jl:656 [inlined]
  [5] getindex
    @ .\broadcast.jl:610 [inlined]
  [6] copy
    @ .\broadcast.jl:912 [inlined]
  [7] materialize
    @ .\broadcast.jl:873 [inlined]
  [8] (::var"#14#16"{Vector{Float32}, Vector{Float32}})(β::Vector{Float32})
    @ Main .\REPL[70]:8
  [9] value!!(obj::NonDifferentiable{Float32, Vector{Float32}}, x::Vector{Float32})
    @ NLSolversBase C:\Users\MrJSa\.julia\packages\NLSolversBase\kavn7\src\interface.jl:9
 [10] initial_state(method::NelderMead{Optim.AffineSimplexer, Optim.AdaptiveParameters}, options::Optim.Options{Float64, Nothing}, d::NonDifferentiable{Float32, Vector{Float32}}, initial_x::Vector{Float32})
    @ Optim C:\Users\MrJSa\.julia\packages\Optim\tP8PJ\src\multivariate\solvers\zeroth_order\nelder_mead.jl:171
 [11] optimize(d::NonDifferentiable{Float32, Vector{Float32}}, initial_x::Vector{Float32}, method::NelderMead{Optim.AffineSimplexer, Optim.AdaptiveParameters}, options::Optim.Options{Float64, Nothing})
    @ Optim C:\Users\MrJSa\.julia\packages\Optim\tP8PJ\src\multivariate\optimize\optimize.jl:36
 [12] optimize(f::Function, initial_x::Vector{Float32}; inplace::Bool, autodiff::Symbol, kwargs::Base.Pairs{Symbol, Union{}, Tuple{}, NamedTuple{(), Tuple{}}})
    @ Optim C:\Users\MrJSa\.julia\packages\Optim\tP8PJ\src\multivariate\optimize\interface.jl:90
 [13] optimize(f::Function, initial_x::Vector{Float32})
    @ Optim C:\Users\MrJSa\.julia\packages\Optim\tP8PJ\src\multivariate\optimize\interface.jl:83
 [14] get_β(α::Vector{Float32}, x::Vector{Float32})
    @ Main .\REPL[70]:11
 [15] (::var"#15#17"{Vector{Float32}})(α::Vector{Float32})
    @ Main .\REPL[70]:17
 [16] value!!(obj::NonDifferentiable{Float32, Vector{Float32}}, x::Vector{Float32})
    @ NLSolversBase C:\Users\MrJSa\.julia\packages\NLSolversBase\kavn7\src\interface.jl:9
 [17] initial_state(method::NelderMead{Optim.AffineSimplexer, Optim.AdaptiveParameters}, options::Optim.Options{Float64, Nothing}, d::NonDifferentiable{Float32, Vector{Float32}}, initial_x::Vector{Float32})
    @ Optim C:\Users\MrJSa\.julia\packages\Optim\tP8PJ\src\multivariate\solvers\zeroth_order\nelder_mead.jl:171
 [18] optimize(d::NonDifferentiable{Float32, Vector{Float32}}, initial_x::Vector{Float32}, method::NelderMead{Optim.AffineSimplexer, Optim.AdaptiveParameters}, options::Optim.Options{Float64, Nothing})
    @ Optim C:\Users\MrJSa\.julia\packages\Optim\tP8PJ\src\multivariate\optimize\optimize.jl:36
 [19] optimize(f::Function, initial_x::Vector{Float32}; inplace::Bool, autodiff::Symbol, kwargs::Base.Pairs{Symbol, Union{}, Tuple{}, NamedTuple{(), Tuple{}}})
    @ Optim C:\Users\MrJSa\.julia\packages\Optim\tP8PJ\src\multivariate\optimize\interface.jl:90
 [20] optimize(f::Function, initial_x::Vector{Float32})
    @ Optim C:\Users\MrJSa\.julia\packages\Optim\tP8PJ\src\multivariate\optimize\interface.jl:83
 [21] get_α(x::Vector{Float32})
    @ Main .\REPL[70]:22
 [22] top-level scope
    @ REPL[71]:1